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Mirrors > Home > ILE Home > Th. List > Mathboxes > ax-bdsb | GIF version |
Description: A formula resulting from proper substitution in a bounded formula is bounded. This probably cannot be proved from the other axioms, since neither the definiens in df-sb 1743, nor probably any other equivalent formula, is syntactically bounded. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdsb.1 | ⊢ BOUNDED 𝜑 |
Ref | Expression |
---|---|
ax-bdsb | ⊢ BOUNDED [𝑦 / 𝑥]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . 3 wff 𝜑 | |
2 | vx | . . 3 setvar 𝑥 | |
3 | vy | . . 3 setvar 𝑦 | |
4 | 1, 2, 3 | wsb 1742 | . 2 wff [𝑦 / 𝑥]𝜑 |
5 | 4 | wbd 13387 | 1 wff BOUNDED [𝑦 / 𝑥]𝜑 |
Colors of variables: wff set class |
This axiom is referenced by: bdab 13413 bdph 13425 bdsbc 13433 bdcriota 13458 |
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